A semiconductor memory device that permits only sequential access to the data cells of a memory array, such as an EEPROM, is known. This type of semiconductor memory device is used as a memory device for storing data pertaining to the amount of consumables remaining or the amount consumed because it is relatively inexpensive. Furthermore, a technology is known wherein a prescribed data storage area is made write-prohibited (i.e., such area is made read-only) by storing map information for the write-prohibited area in a prescribed area in the memory array of the semiconductor memory device after initial data is written to the prescribed data storage area of such memory array.